Determining Manipulated Co-ordinates.

Hey, I ran across this question in my text book.

Dikembe has reflected the gunction g(x) = x^3 in the x-axis, vertically compressed it by a factor of 2/3, horizontally translated it 13 units to the right, and vertically translated it 13 units down. Three points on the resulting curve are (11, -23/3) , (13,-13), abd (15,-55/3). Determine the original co-ordinates of these three points on g(x).

So I concluded the following transformed cubic function f(x) = 2/3 (x-13)^3 -13 , and the equation to convert both x and y co-ordinates back to their original (x-13, 3/2y+13). Now in the textbook, the answers are (-2,8) , (0,0) and (2,-8). My equation works for getting the correct x - int , but not the y. Where did I go wrong?

Would it be a better idea to use the original function g(x) to find the corresponding y-value to the found x values? But If I do we would get (-2,-8) , (0,0) and (2,8).